Triangle T(n, k) = binomial(n, k) * Sum_{j=k..n} StirlingS1(n, j)*StirlingS1(j, k), read by rows.

Terms

a(0) =1a(1) =-4a(2) =1a(3) =21a(4) =-18a(5) =1a(6) =-140a(7) =240a(8) =-48a(9) =1a(10) =1140a(11) =-3150a(12) =1300a(13) =-100a(14) =1a(15) =-11004a(16) =43620a(17) =-29700a(18) =4800a(19) =-180a(20) =1a(21) =123074a(22) =-650769a(23) =647780a(24) =-175175a(25) =13965a(26) =-294a(27) =1a(28) =-1566928a(29) =10517108